A central question in perceptual and cognitive psychology is the nature of the processes that combine the multiple sources of environmental information in order to support the subjective, unitary percepts of objects. One of the more promising extant approaches is known as general recognition theory (GRT). GRT provides formal, mathematically-specified definitions of the ways in which perceptual dimensions (e.g., the various elements of a face) can interact during perception and identification, and generalizes the signal-detection-based distinction between perceptual and decisional effects to multidimensional stimuli. Although the formalisms of GRT provide clear definitions and distinctions, there are only a limited set of quantitative and statistical methodologies available for relating theory to data, and there have been (to date) no attempts to comprehensively assess the relative strengths and weaknesses of these approaches. The work presented here is an initial attempt providing this comprehensive assessment. We consider three approaches to the question of model estimation and recovery. The first, based on work by Ashby, Kadlec, and Townsend, involves application of a set of measures applied to response frequencies drawn from signal detection theory. The second, based on work by Maddox, Ashby, and Thomas, involves the numerical estimation of model parameters under a variety of constraints. The third approach, based on work by De Carlo and Rouder, involves estimation in terms of novel extensions to standard statistical methods. The approaches are contrasted using data sets with known configurations, including violations of underlying model assumptions (including mean-shift integrality), and performance is characterized in terms of rates of inferential error, sign and magnitude of statistical bias, and consistency and efficiency. In addition, the models are contrasted using published data sets. The results of these efforts are used to highlight weaknesses in current approaches that require further work.